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Math
234: Fukaya Categories
Fall 2025
Syllabus
Fukaya categories occupy a central role in modern mathematics, at
the junction of algebraic geometry, symplectic geometry,
low-dimensional topology, and mathematical physics. The goal
of this course is to give an introduction to Lagrangian Floer
homology, Fukaya categories, and homological mirror symmetry.
Instructor: Ko Honda
Office Hours: TBA
E-mail: honda at math dot ucla dot edu
URL: http://www.math.ucla.edu/~honda
Class Meetings: Lectures are MWF 9-9:50am at MS 5137
Topics
- Some
symplectic geometry
- Lagrangian
Floer (co-)homology
- A-infinity
algebras and A-infinity categories
- Construction
of the Fukaya categories and some variants including the
wrapped Fukaya category
- Exact
triangles, twists, split generation
- Homological
mirror symmetry e.g. of the torus
Prerequisites:
Math 225 sequence or equivalent (a good knowledge of
differentiable manifolds and homology). Some knowledge of
symplectic geometry is helpful, but not necessary.
Grading: TBA
References
Basics of symplectic geometry:
- D.
McDuff and D. Salamon, Introduction to symplectic topology,
2nd edition, Oxford Mathematical Monographs. The Clarendon
Press, Oxford University Press, New York, 1998.
- A.
Cannas da Silva, Lectures
on symplectic geometry.
A-infinity
algebras:
- B.
Keller, Introduction
to A-infinity algebras and modules.
Fukaya categories:
- D. Auroux, A
beginner's introduction to Fukaya categories.
- P. Seidel, Fukaya categories and Picard-Lefschetz theory.
WARNING: The course syllabus provides a general plan for the
course; deviations may become necessary.
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Last modified: August 27, 2025. |